Optimal oscillation-center transformations
The author considers Hamiltonian systems with the Hamiltonian of the form \(H_ 0(p)+H_ 1(q,p,t)\) and defines an ''optimization'' criterion for canonical transformations, continuously connected with identity, such that new P and Q are to be as close as possible (in a suitable sense) to traditional action-angle or oscillation-center variables. A variational principle is proposed, which is based on minimization of mean square generalized force over phase space and time. The optimal oscillation- center transformation for physical pendulum is constructed analytically. A modified principle for relativistic systems is presented in an Appendix.
minimization of mean square generalized force
optimal oscillation-center transformation
scientific article; zbMATH DE number 3958790
scientific article